There are two seperate endings that may be unlocked in Odin Sphere, depending on how the player plays through the final book, Armageddon.

Good Ending: In order to unlock the good ending, you must use the characters in the following order: Cornelius, Oswald, Mercedes, Velvet, Gwendolyn. So Cornelius must fight the "Six-Eyed Beast," Oswald must fight the "Lord of the Netherworld," Mercedes must defeat the "Incarnation of Fire," Velvet must fight "The Cauldron" and Gwendolyn must kill "The Last Dragon."

Bad Ending: In order to unlock the bad ending, use the characters in any order except for the one listed for the Good Ending.